The Southampton to Glasgow flight lasted well into One-Eleven days, and indeed into British Caledonian times.
You can thumb through old Jersey Airlines, BUA and B Cal timetables here (click on the dates rather than the name, and then through the individual pages) :
Airline Timetable Images - List of Complete Timetables
First appearance of the route seems to be in the 1962 timetable of Jersey Airlines, one of BUA's predecessors, operated with a Handley Page Herald. For much of BUA's time it continued to have a Jersey Airlines flight number. I think the paved runway had only just been installed at Southampton by 1962 (it was very late compared to other UK airports), which probably led to the service start.